Polarization mode dispersion compensator and method thereof

ABSTRACT

A polarization transformer in a polarization mode dispersion compensator is adjusted over its changing device characteristics with environmental changes and time by using a feedback signal indicating a state of polarization and a distortion of an output optical signal of compensating optics.

TECHNICAL FIELD

The present invention relates to methods for controlling the state ofpolarization of light. In particular, the present invention relates tocontrol methods which provide endless transformation of any varyingpolarization to a static polarization, or vice versa, control methodsfor the general transformation of any varying to any varyingpolarization, and polarization mode dispersion compensators whichimplement these control methods.

BACKGROUND ART

The higher the bit rate of an optical transmission system, the more aspecific amount of polarization mode dispersion of an optical fiberdistorts the transmitted signal.

Due to polarization mode dispersion, the two modes in a so calledsingle-mode fiber propagate with different velocities. An initial pulsesplits its energy into the two modes. The two modes experience adifferential delay during propagation. This leads to pulse spreading atthe end of the fiber. The more the differential delay between the twomodes is in the order of the bit duration, the more neighboring pulseswill overlap, which leads at least to an increasing bit-error rate oreven makes it impossible to differentiate the pulses. Polarization modedispersion is due to internal birefringence (e.g. fiber core geometryirregularities) or externally induced birefringence (e.g. bending,squeezing, etc.). Because in a long single-mode fiber, polarization modecoupling occurs at randomly varying locations with randomly fluctuatingstrength due to e.g. environmental changes like temperature,polarization mode dispersion itself varies over time. It is well known,that the instantaneous differential group delay between the principalstates of polarization follows a Maxwellian probability densityfunction. The mean of the Maxwellian distributed instantaneousdifferential group delay is known as the average differential groupdelay, or the polarization mode dispersion value (PMD) of the fiber. Thepolarization mode dispersion value is, for long single-mode fibers withhigh polarization mode coupling, proportional to the square root of thefiber length.

To mitigate signal distortion due to polarization mode dispersion,optical elements introducing a similar amount of differential groupdelay as in the fiber but with an opposite sign, can be placed at theend of the fiber. Due to the random nature of the instantaneousdifferential group delay and the principal states of polarization in along optical fiber, the optical elements used for compensatingpolarization mode dispersion must be adaptively adjusted to themomentary fiber conditions. A closed loop design, polarization modedispersion compensator consequently consists of:

1. polarization transformer

2. PMD compensating optical elements (adaptive optics)

3. distortion analyzer

4. control logic as depicted in FIG. 1.

In FIG. 1, the distortion analyzer 14 provides a measure of signaldistortion for the control logic 13 to adaptively adjust thepolarization transformer 11 and the adaptive optics 12, such that theybest match the momentary polarization mode dispersion conditions of theoptical fiber.

Besides methods like, for example, spectral hole burning (SHB), directeye-opening analyzing, etc., the degree of polarization (DOP) can beused for analyzing signal distortion due to polarization modedispersion. For those who are skilled in the art, it is well known thata light beam experiences depolarization if the coherence length, whichis inversely proportional to the spectral width, is in the order of thedifferential group delay. The higher the differential group delaybecomes compared to the coherence length, the more the beam getsdepolarized and its degree of polarization decreases. This well knownphysical effect is straightforward to be used as a feedback signal toadaptively control optical elements of a polarization mode dispersioncompensator. Derivation of the depolarization of an optical signal dueto fiber anisotropies as a function of signal spectrum (bandwidth,form), differential group delay and state of input polarization is shownin non-patent document 1.

Compared to spectral hole burning, measuring directly the eye-opening orbit-error rate detection, the advantages of using the degree ofpolarization as a feedback signal for adaptive polarization modedispersion compensation are:

1. independent of bit rate

2. applicable to any modulation format without requiring modifications

3. insensitive to chromatic dispersion, such that degree of polarizationprovides a good measure of signal distortion due to only polarizationmode dispersion

Depicted in FIG. 2 are, as a function of instantaneous differentialgroup delay, the degree of polarization and Q-penalty of a transmittedsignal, non-return to zero (NRZ) format modulated with a bit rate of 48Gbit/s. The Q-penalty is defined here as: $\begin{matrix}{{Q\text{-}{penalty}} = {{20 \cdot \log}{\frac{{Eye}\text{-}{opening}\quad{of}\quad{received}\quad{signal}}{{Back}\text{-}{to}\text{-}{back}\quad{eye}\text{-}{opening}}.}}} & (1)\end{matrix}$

For reference, also shown in FIG. 2 is the power of the 24 GHz (half thebit rate) spectral component as a function of instantaneous differentialgroup delay. The spectral component at half the bit rate has been provedto show the strongest dependence on instantaneous differential group.

Contrary to the degree of polarization which shows only one maximum ifthe instantaneous differential group delay vanishes, the 24 GHz spectralcomponent shows a periodic behaviour. Therefore, in cases where theinstantaneous differential group delay is expected to exceed on bitduration, at least one more spectral component, namely the 12 GHz(quarter of the bit rate) must be additionally tested to avoid anambiguity.

The details of the degree of polarization and the power of spectralcomponents at 24 GHz (half the bit rate), 12 GHz (quarter of the bitrate) and 6 GHz (eighth the bit rate) are depicted in FIG. 3 for smallvalues of the instantaneous differential group delay.

FIG. 4 shows one configuration of a polarization transformer to realizegeneral polarization transformation from one arbitrary varying inputpolarization to any varying output polarization. This configurationconsists of 4 variable retarders 41, 42, 43, and 44 with fixed eigenaxisoriented at 0°, 45°, 0°, and 45°, respectively. Input light 45 passesthrough these retarders to be output as output light 46.

Provided that each of the retarders has an adjustment range of 4π,polarization transformation from one arbitrary varying inputpolarization to any varying output polarization is possible. But, if oneof the retarders reaches an adjustment limit, i.e. the desiredtransformation requires adjustment in excess of the provided range,rewind operation is necessary. During the rewind operation, the retarderthat reached its limit needs to be continuously brought back to a statewhich is far from the adjustment limit while the remaining threeretarders have to take over polarization control. This kind of operationtakes processing time which slows down the response speed topolarization fluctuations.

If a rewind operation needs to be performed in a situation where fastfluctuations appear to happen, polarization control may becomeimpossible due to limited processing speed. For this reason, it isdesirable to realize a polarization transforming apparatus which does inprincipal not require rewind operations.

To realize a general polarization transformation from one arbitraryvarying input polarization to any varying output polarization withoutrequiring rewind operations, several configurations exist (seenon-patent document 2, for example).

FIG. 5 shows one configuration to realize such a general polarizationtransformation. This configuration consists of freely rotatable λ/4-,λ/2-, and λ/4-waveplates 51, 52, and 53 and is known to provide endlesspolarization transformations for one, and only one specific wavelengthat which the waveplates introduce phase shifts of π/2, π, and π/2. Inputlight 54 passes through these waveplates to be output as output light55.

The stringent requirement of exact phase shifts limits the usability ofthis configuration to only a very small wavelength range. Furtherlimitations arise from the required mechanics, making this configurationvery slow.

The basic structure for realizing a polarization transforming device ona lithium niobate (LiNbO₃) substrate is depicted in FIG. 6. It consistsof a LiNbO₃ substrate 65, waveguide 64, buffer layer 66, and threeelectrodes 61, 62, and 63. The optical signal passes through thewaveguide.

Grounding the center electrode 62 and applying positive or negativevoltages to the outer electrodes 61 and 63 introduces a horizontalelectrical field in the waveguide (x-direction). Applying voltages withreverse sign to the outer electrodes 61 and 63 introduces a verticalelectrical field in the waveguide (y-direction). In a x-cut,z-propagating LiNbO₃ substrate, these electrical fields change therefractive indices over the electro-optic coefficient r₁₂.

Defining three voltages which describe the device characteristics

V_(bias) is the voltage for which intrinsic birefringence is canceled

V₀ is the voltage for which full transverse electric-transverse magnetic(TE-TM) mode conversion takes place

V_(π) is the voltage for which a phase shift of 180 degrees between theTE- and TM-mode is introduced,the device can be controlled to behave like an endless rotatable1/n-waveplate with a rotation angel θ/2. To achieve this, the voltage V₁applied to the electrode 61 and the voltage V₃ applied to the electrode63 calculate as: $\begin{matrix}{V_{1} = {{\frac{V_{0}}{n/2}\sin\quad(\theta)} - {\frac{V_{\pi}}{n}\cos\quad(\theta)} - \frac{V_{bias}}{2}}} & (2) \\{V_{3} = {{\frac{V_{0}}{n/2}\sin\quad(\theta)} + {\frac{V_{\pi}}{n}\cos\quad(\theta)} + \frac{V_{bias}}{2}}} & (3)\end{matrix}$This guarantees, in theory, operation like an endless rotatablewaveplate. Because of applying the voltages in aperiodic fashion,control limits are never reached. Therefore, rewind operations are neverrequired. What is required to guarantee the operation as an endlessrotatable waveplate, is the knowledge of the device characteristics interms of the voltages V_(bias), V₀, and V_(π).

Although these voltages can be acquired by measurement, they are subjectto changes. In practice, these voltages not only depend on temperatureand wavelength. Due to a drift caused by applying a direct-current (DC)voltage to such devices, the device characteristics change. Inparticular, the voltage Vbias is subject to change due to DC drift. Overtime, device characteristics described in terms of the voltagesV_(bias), V₀, and V_(π) change. The initial set of voltages derived froma measurement become therefore invalid and operation of the device likean endless rotatable waveplate is no longer possible.

If a method is found which can derive the characteristics of the deviceduring normal operation, the basic structure shown in FIG. 6 can be usedto realize a polarization transformer with the principal capability oftransforming any varying input polarization to any varying outputpolarization. Such a device is shown in FIG. 7. It consists of a LiNbO₃substrate 81, waveguide 80, and three electrode sections. The first,second, and third section includes electrodes 71 through 73, 74 through76, and 77 through 79, respectively. Grounding all center electrodes 72,75, and 78 and applying voltages V₁, V₂, V₃, V₄, V₅, and V₆ to the outerelectrodes 71, 73, 74, 76, 77, and 79, respectively in the form of$\begin{matrix}{V_{1} = {{\frac{V_{0}}{2}\sin\quad(\alpha)} - {\frac{V_{\pi}}{4}\cos\quad(\alpha)} - \frac{V_{bias}}{2}}} & (4) \\{V_{2} = {{\frac{V_{0}}{2}\sin\quad(\alpha)} + {\frac{V_{\pi}}{4}\cos\quad(\alpha)} + \frac{V_{bias}}{2}}} & (5) \\{V_{3} = {{V_{0}\sin\quad(\beta)} - {\frac{V_{\pi}}{2}\cos\quad(\beta)} - \frac{V_{bias}}{2}}} & (6) \\{V_{4} = {{V_{0}\sin\quad(\beta)} + {\frac{V_{\pi}}{2}\cos\quad(\beta)} + \frac{V_{bias}}{2}}} & (7) \\{V_{5} = {{\frac{V_{0}}{2}\sin\quad(\gamma)} - {\frac{V_{\pi}}{4}\cos\quad(\gamma)} - \frac{V_{bias}}{2}}} & (8) \\{{V_{6} = {{\frac{V_{0}}{2}\sin\quad(\gamma)} + {\frac{V_{\pi}}{4}\cos\quad(\gamma)} + \frac{V_{bias}}{2}}},} & (9)\end{matrix}$the whole structure is operated like freely rotatable λ/4-, λ/2-, andλ/4-waveplates oriented at the angles α, β, and γ, respectively. Thecharacteristic voltages V_(bias), V₀, and V_(π) may differ for each ofthe three sections.

In the following, problems of the conventional polarization control aresummarized.

The emphasis is on the application of polarization control for adaptivecompensation of polarization mode dispersion (PMD) in high-speed opticaltelecommunication systems. PMD is well known to cause a spread ofoptical pulses during transmission. The two polarization modes in anoptical fiber experience a differential group delay manifesting in pulsespreading. In order to compensate for PMD, a polarization controller(polarization transformer) followed by a differential group delay (DGD)element can be used. In this case, birefringent crystals like yttriumorthovanadate (YVO₄), titanium dioxide (TiO₂), calcium carbonate(CaCO₃), etc., or polarization maintaining fiber (PMF) are used as a DGDelement. To compensate for PMD, the polarization controller has to beadjusted such that it transforms the fast eigenaxis of the DGD elementto match the slow output principal state of polarization (PSP) of thetransmission system. In this case, the DGD of the transmission fiber isreduced by the amount of DGD introduced by the DGD element following thepolarization controller. In a second method, the polarization controllerhas to be adjusted such that the input PSP of the transmission fibermatches the state of polarization of the launched optical signal bytransforming the eigenaxis of the DGD element in an appropriate way.Whatever method is used, required is the capability of endlesstransformation of the linear eigenaxis of the DGD element in order tofollow arbitrary changes of the transmission fiber's PSP due toenvironmental influences.

As described above, two types of methods can be distinguishedinprincipal for endless, reset-free polarization control:

1. those requiring rewind operations

2. those not requiring rewind operations

A device which requires rewind operations consists, for example, of fourretarders oriented at 0°, 45°, 0°, and 45° with a retardation adjustmentrange of 4π. In this case, a fiber-squeezer, lead lanthanum zirconatetitanate (PLZT), a liquid crystal (LC), or a Faraday rotator is used asa retarder. If, during operation, one of the retarders reaches a controllimit, it must be rewound. This rewind operation is always possible forthe above described device in the case the required operation is totransform any varying state of polarization to a static polarization, orvice versa. But, rewinding takes processing time and may fail if fastfluctuations occur or the application requires transformation of anyvarying polarization to any varying polarization.

A device which does not require rewind operations consists for exampleof a combination of endless rotatable quarter-, half-, andquarter-waveplate. To assure proper operation, the retardation of thewaveplates is required to be exact. As a consequence, this device isonly applicable for a very limited wavelength range. Furthermore,required mechanics make it a slow solution. Faster solutions are deviceswhich either consist of five variable retarders oriented at 0°, 45°, 0°,45°, and 0° (LC, PLZT, etc.) or 3-electrode structure LiNbO₃ baseddevices. Such devices provide in principal endless, reset-free operationif, and only if, the device properties (change of device characteristicswith applied control signals) are well known. Calibration is possible,but only applicable in a stable environment and for a short time(temperature dependence, DC drift, ageing, etc.). These types ofproblems have also been discussed in other patent documents (see patentdocuments 1, 2, and 3, for example).

Because polarization controllers that do not require rewind operationsdo provide in principal the fastest and most reliable way ofpolarization control, devices constructed and controlled in a way thatthey always reliably provide desired transformation capability areparticularly interesting. Applications of the devices include fastpolarization control (stabilization) and fast PMD compensation.

Non-Patent Document 1

Jun-ichi Sakai, Susumu Machida, Tatsuya Kimura, “Degree of Polarizationin Anisotropic Single-Mode Optical Fibers: Theory”, IEEE Journal ofQuantum Electronics, Vol. QE-18, No. 4, pp. 488-495, 1982

Non-Patent Document 2

N. G. Walker and G. R. Walker, “Polarization control for coherentcommunications”, Journal of Lightwave Technology, Vol. 8, No. 3, pp.438-458, 1990

Patent Document 1

published Japanese translation of PCT international publication forpatent application (WO00/36459), No. 2002-532752

Patent Document 2

publication of Japan patent application, No. 2001-244896

Patent Document 3

publication of Japan patent application, No. 2002-033701

DISCLOSURE OF INVENTION

It is an object of the present invention to provide a polarizationcontrol method to overcome the problem of changing devicecharacteristics with environmental changes and time, and a polarizationmode dispersion compensator which implements such a method.

In the first aspect of the present invention, the polarization modedispersion compensator comprises a polarization transformer, acompensating optical unit, a distortion analyzer, and a control circuit.The polarization transformer transforms polarization of an input opticalsignal and the compensating optical unit compensates for a polarizationmode dispersion of the input optical signal and outputs an outputoptical signal. The distortion analyzer measures a state of polarizationand a distortion of the output optical signal and generates a feedbacksignal indicating the measured state of polarization and distortion. Thecontrol circuit generates, based on the feedback signal, control signalsfor adjusting the polarization transformer in such a way that aplurality of target states of polarization in which the distortion ismeasured are realized in output optical signals in following operations.

In the second aspect of the present invention, the distortion analyzermeasures a degree of polarization of the output optical signal asdistortion information. Then, the control circuit generates the controlsignals for adjusting the polarization transformer in such a way that anoptimum state is found from among the target states of polarization bysearching for a state with the maximum degree of polarization in acircumference of an actual state in a polarization space.

In the third aspect of the present invention, the distortion analyzermeasures a degree of polarization of the output optical signal asdistortion information. Then, the control circuit records the measuredstate of polarization and degree of polarization, and calculates frompolarization changes control signals for adjusting the polarizationtransformer in such a way that the target states of polarization areequally separated from each other and equally distant from the actualstate in the polarization space. In this case, the target states ofpolarization may be preset and located on a circle around the actualstate at a predefined distance in the polarization space.

In the fourth aspect of the present invention, the distortion analyzermeasures a degree of polarization of the output optical signal asdistortion information. Then, the control circuit records the measuredstate of polarization and degree of polarization, calculates frompolarization changes control signals for adjusting the polarizationtransformer in such a way that the target states of polarization areunequally separated from each other and unequally distant from theactual state in the polarization space, and weights measured degrees ofpolarization in the target states of polarization by using a distancebetween each target state of polarization and the actual state in thepolarization space.

In the fifth aspect of the present invention, the control circuitrecognizes changing device characteristics of the polarizationtransformer in a case where a part of the target states of polarizationare not be realized, and takes countermeasures such that thepolarization transformer operates like endless rotatable waveplates byrecalculating a voltage which describes the device characteristics ofthe polarization transformer and generating a control signal forapplying the calculated voltage to the polarization transformer.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a configuration of a conventional polarization modedispersion compensator.

FIG. 2 shows degree of polarization, Q-penalty and a spectral componentas a function of instantaneous differential group delay.

FIG. 3 shows detail of degree of polarization, Q-penalty and a spectralcomponent as a function of instantaneous differential group delay.

FIG. 4 shows a configuration of a polarization transformer whichconsists of 4 variable retarders.

FIG. 5 shows a configuration of a polarization transformer whichconsists of 3 rotatable waveplates.

FIG. 6 shows a basic structure of a polarization transformer on a LiNbO₃substrate.

FIG. 7 shows a basic structure of a polarization transformer on a LiNbO₃substrate with the capability of transforming any varying inputpolarization to any varying output polarization.

FIG. 8 shows a configuration of a polarization mode dispersioncompensator which employs a degree of polarization as information of asignal distortion.

FIG. 9 shows a flowchart of an operation of a polarization modedispersion compensator.

FIG. 10 shows search for an optimum state on a Poincaré-sphere.

FIG. 11 shows search for an optimum state in a 2-dimensionalpolarization space.

FIG. 12 shows another search for an optimum state on a Poincaré-sphere.

FIG. 13 shows another search for an optimum state in a 2-dimensionalpolarization space.

FIG. 14 shows a situation in which desired polarizations are not able tobe reached.

FIG. 15 shows a concrete example of a configuration of a polarizationmode dispersion compensator.

FIG. 16 shows a configuration of a polarization mode dispersioncompensator which employs a photodiode and a band-pass filter to detecta signal distortion.

FIG. 17 shows a configuration of a polarization mode dispersioncompensator which employs a forward error correction unit to detect asignal distortion.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, preferred embodiments according to the present inventionwill be described in detail by referring to the drawings.

To overcome the problem of changing device characteristics withenvironmental changes and time, a method using the information providedby a polarimeter, which is used anyway in an advantageous realization ofa PMD compensator for feedback, is employed. Integration of the methodinto the timing of the control makes it possible to apply it withoutincreasing processing time or demanding more sophisticated controllogic.

Although a degree of polarization (DOP) as a measure of signaldistortion due to polarization mode dispersion can be used to control aPMD compensator, it is advantageous to use additional information on thestate of polarization—in particular the variation of the state ofpolarization with the changing control signals applied to thepolarization transformer—to compensate for changing characteristics ofthe polarization transformer. In the following, various methods will bedescribed for applying the DOP as a feedback signal to adaptivepolarization mode dispersion compensators (PMDCs) and using theadditional information on the state of polarization for advantageousrealization of the control algorithm that is tolerant to changing devicecharacteristics.

Assuming the PMDC is initially in an optimum state, i.e. it compensatesfor distortion due to PMD to the best of the ability of the compensatingoptics, this optimum state corresponds to a maximized DOP. Additionally,the state of polarization as measured by the polarimeter is known. Thisstate of polarization is fully described by two variables (angles): theazimuth θ and the ellipticity ε. If the PMD condition of thetransmission span in front of the PMDC changes, both the DOP and thestate of polarization will change. The PMDC is then no longer in anoptimum state. In order to find the new optimum state, i.e. controlsignals applied to the polarization transformer and the compensatingoptics, the PMDC has to test the DOP in the circumference of the oldoptimum state. This can be done by applying slightly changed controlsignals while searching for those changes that lead to an increase ofthe DOP. Two problems arise using this simple approach in practicalsystems:

-   1. Due to changing characteristics of the polarization transforming    device, it cannot be guaranteed that the required transformation for    adjusting the PMDC to its optimum state is possible. Worse still, by    only using the DOP as a measure of signal distortion and for    providing feedback to the control logic, it is not even possible to    identify those situations in which a required transformation cannot    be performed. This problem is not limited to the use of DOP as the    feedback signal for a PMD compensating device. It also applies to    other feedback methods like spectral-hole burning, eye-opening    measurement, orbit-error rate. All these methods only provide a    measure of distortion.-   2. Changing the control signals by predefined steps does by no means    imply, that the PMDC changes its compensating state by distinct    steps. In fact, depending on the PMD condition of the transmission    span, and the state of the PMDC, a change of one control signal    might lead to only a very small change of the compensating state of    the PMDC. Even situations in which any change of one control signal    does not lead to any change in the compensating state of the PMDC    might appear. For example, such situations happen, if the    polarization to be transformed comes close to an eigenaxis of one of    the sections of the polarization transforming device.

To overcome the problems associated with 1 and 2, the polarizationtransforming device of a PMDC is controlled according to the followingdescription. Initially, the PMDC is set to a condition at which itcompensates for PMD to the best of the capability of the compensatingoptics by finding the maximum DOP. This is performed by adjusting thepolarization transforming device such that the polarizations as measuredby the polarimeter cover the whole Poincaré-sphere (−45°≦Ellipticityε<45°, −90°≦Azimuth θ<90°) and calculating the DOP value. From theresulting 2-dimensional map of DOP values versus azimuth andellipticity, the global maximum for the DOP is known. The polarizationtransformer of the PMDC is set to the condition corresponding to thismaximum DOP value. In the case where the compensating optics provideadditional adjustment capability, i.e. added degrees of freedom, thecontrol parameters can be successively changed while taking the2-dimensional DOP map to find the global optimum. The operationdescribed above to find the global optimum is only allowed at times thePMDC is switched on. During the operation of a transmission system, thePMDC is not allowed to scan through all its possible states for findingthe global maximum because this operation introduces high distortions tothe optical signal. During the operation of a transmission system, thePMDC is required to track changing PMD conditions, and find its optimumstate without introducing unacceptable signal distortions. Dithering thecontrol signals (applying small changes to the control signals) would beone method to track the optimum state. Due to changing devicecharacteristics (ageing, temperature, etc.) the problems described abovewill occur in practical applications. To overcome those problems, in anadvantageous method optimization of the state of the polarizationtransforming device is not performed over the space of control signals,but over the space of polarizations as measured by the polarimeter.

FIG. 8 shows a configuration of a PMDC employing the advantageousmethod. The PMDC comprises polarization transformer 82, adaptive optics83, control circuit 84, and polarimeter 85. Input light 86 passesthrough the polarization transformer 82 and the adaptive optics 83 to beoutput as output light 87. The polarimeter 85 corresponds to thedistortion analyzer 14 in FIG. 1 and measures the state and degree ofpolarization of the output light 87 to generate a feedback signal. Thecontrol circuit 84 generates control signals for the polarizationtransformer 82 and the adaptive optics 83 using the feedback signal fromthe polarimeter 85.

Describing the state of polarization in terms of the Stokes-vector{right arrow over (S)} $\begin{matrix}{{\overset{->}{S} = \begin{pmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{pmatrix}},} & (10)\end{matrix}$the DOP is calculated as the quotient of the polarized light power andthe total power: $\begin{matrix}{{DOP} = {\frac{\sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}}}{S_{0}}.}} & (11)\end{matrix}$

This PMDC operates according to the flowchart shown in FIG. 9. First,the polarimeter 85 measures the initial Stokes-vector and DOP at theinitial optimum position in a polarization space (Step 91). An exampleof the initial optimum position A0 on the Poincaré-sphere is depicted inFIG. 10. FIG. 11 shows another view of A0 in a 2-dimensional space ofangles θ and ε.

The control circuit 84 drives the polarization transformer 82 such thatStokes-vectors are on a circle around A0 and memorizes associated DOPvalues (Step 92). In FIGS. 10 and 11, 8 target positions A1 through A8are located on the circle around A0 for example. Then, the controlcircuit 84 checks whether all the target positions could be realized(Step 93). If one of the target positions could not be realized, thecontrol circuit 84 changes the device characteristics of thepolarization transformer 82 (Step 94) and repeats the operations in andafter Step 92. In the case where a polarization transforming device on aLiNbO₃ substrate as shown in FIG. 6 is used, control signals to changeV_(bias), V₀, and V_(π) are output to the polarization transformer 82.If all the target positions could be realized, the control circuit 84drives the polarization transformer 82 such that Stokes-vector is theone with the maximum associated DOP among the Stokes-vectors for thetarget positions (Step 95) and repeats the operations in and after Step92 with the position of the maximum DOP as a new initial position. Inthe case where A4 among A1 through A8 is associated with the maximumDOP, this position becomes the new initial position B0 as shown in FIG.12 and new target positions B1 through B8 are to be realized.

According to the above-described control, starting from the initialoptimum state, the control signals applied to the polarizationtransformer 82 are adjusted such that the polarizations as measured bythe polarimeter 85 are located on a circle around the intial optimumposition A0. From the measured DOP values at each of the positions A1through A8, the direction pointing to the new optimum state iscalculated. If the PMD condition of the transmission system has notchanged, all the DOP values at A1 through A8 are lower than the DOPvalue at the initial state. The polarization transformer 82 is thenredirected to this initial state, from which it starts again to probethe DOP values in the circumference of the initial polarization. If thePMD condition has changed, at least one of the DOP values measured at A1through A8 is higher than the initial DOP value. The polarizationtransformer 82 is then adjusted to this new state from which it startsagain to probe the DOP values in the circumference of the new state.Repeating the above steps over and over again, the polarizationtransforming device of the PMDC tracks changing PMD conditions of thetransmission system. In order to find the control signals leading toequally separated states in the polarization space at which the DOPvalue is probed, the control starts with an arbitrary initial set ofcontrol signals. Both the control signals and the changes in the stateof polarization are recorded. With the knowledge of what control signalslead to what polarization changes, the next set of control signals canbe calculated such that in the next sequence polarizations come closerto the ideal condition of equal separation. Repeating this operationover and over again, the set of control signals to be applied forequally separated polarization at which the DOP value is measured isfound. For example, a sub-optimal set of probed polarization states isshown in FIG. 13. Here, C1 through C8 around the initial position C0 arerealized and only the polarization at C1 appears to be in an idealdistance to the actual polarization. Subsequent states are at a reduceddistance. The algorithm calculates from the known distances new sets ofcontrol signals, such that at next operations short distantpolarizations are located farther away from the actual state.

A situation which appears to happen if the device characteristics of thepolarization transformer 82 have changed, is shown in FIG. 14. Althoughpolarizations at the positions D1 through D8 are realized in thecircumference of the actual state at the position D0, the controlalgorithm is by no means able to reach the desired polarizations 141 bycontrolling the polarization transformer 82 in a way such that itoperates like endless rotatable waveplates using the device describingvoltages. Experiencing such a situation, the control algorithm slightlyvaries the voltages describing the device characteristics of thepolarization transformer 82 such that all the target polarizations arelocated again on a circle around the initial polarization. Because thetarget polarizations are given (they have to be located on a circlearound the initial state), situations at which the devicecharacteristics of the polarization transformer 82 are changed canalways be recognized.

FIG. 15 shows a concrete example of the configuration of the PMDC shownin FIG. 8. The PMDC comprises polarization transforming device 1501,polarization maintaining fibers 1502 (0°) and 1504 (90°), controlcircuit 1505, variable retarder 1503 (45°), beam splitter 1506, retarder1507 (π/4), polarizers 1508 (0°), 1509 (45°), and 1510 (0°), andphotodiodes 1511 through 1514. The polarization transforming device 1501and the control circuit 1505 correspond to the polarization transformer82 and the control circuit 84 in FIG. 8, respectively. The polarizationmaintaining fibers 1502 and 1504 and variable retarder 1503 correspondsto the adaptive optics 83 in FIG. 8. The beam splitter 1506, retarder1507, polarizers 1508 through 1510, and photodiodes 1511 through 1514form the polarimeter 85 in FIG. 8.

The polarization transforming device 1501 is realized by at least threeor multiple three-electrode structures on a LiNbO₃ substrate as shown inFIG. 7. The adaptive optics comprise two sections of differential groupdelay introducing elements 1502 and 1504 separated by a variableretarder 1503 and the eigenaxis of the variable retarder 1503 isoriented at 45° with respect to the eigenaxis of each differential groupdelay introducing elements. More generally, the adaptive optics maycomprise multiple sections of differential group delay introducingelements separated by individually controllable variable retarders withthe eigenaxis oriented at 45° with respect to the eigenaxis of each oftwo adjacent differential group delay introducing elements. Denoting theintensities detected by the photodiodes 1511, 1512, 1513, and 1514 asI₀, I₁, I₂, and I₃, respectively, the Stokes-vector {right arrow over(S)} can be obtained by the following equations. $\begin{matrix}{\overset{->}{I} = \begin{pmatrix}I_{0} \\I_{1} \\I_{2} \\I_{3}\end{pmatrix}} & (12) \\{{\overset{->}{S} = {E \cdot \overset{->}{I}}}{E\text{:}\quad{unit}\quad{matrix}}} & (13)\end{matrix}$

Target positions are located on a circle in the above-describedembodiments, however, the proposed method is not limited toStokes-vectors targeted to surround the initial position on a circle. Acircle is the most straightforward shape to implement and does notrequire weighting. Shapes other than a circle require weighting for thedecision of the next initial position. An ellipse, for example, can beused as a shape on which target positions are located. Weighting can beperformed by (but is not limited to) multiplying measured DOP values atpositions A1 through A8 by the inverse distance from the initialposition A0. This is an effective countermeasure against otherwisepossible misjudgements due to underestimating the significance of smallDOP changes for small distances.

Furthermore, it is possible to use other information indicating thesignal distortion as a feedback signal. Examples are shown in FIGS. 16and 17.

The PMDC shown in FIG. 16 comprises polarization transformer 1601,adaptive optics 1602, control circuit 1603, polarimeter 1604, aphotodiode 1605, and a band-pass filter 1606. The polarimeter 1604measures the state of polarization (Stokes-vector) of the output lightto generate a feedback signal. This is required to track whether targetSOPs on a circle around the initial position could be realized. Thephotodiode 1605 detects the output light to generate an electric signaland the band-pass filter 1606 generates a feedback signal for thedecision of a next initial position. The band of the band-pass filter1606 is determined such that a specific frequency component of B/n (B:the bit-rate of the signal light, n=2, 4, 6, . . . ) can be detected.The control circuit 1603 generates control signals for the polarizationtransformer 1601 and the adaptive optics 1602 using the feedback signalsfrom the polarimeter 1604 and the band-pass filter 1606.

The PMDC shown in FIG. 17 comprises polarization transformer 1701,adaptive optics 1702, control circuit 1703, and polarimeter 1704.Receiver unit 1705 and forward error correction (FEC) unit 1706 areprovided in the receiver side. The polarimeter 1704 measures the stateof polarization (Stokes-vector) of the output light to generate afeedback signal as in the configuration shown in FIG. 16. The forwarderror correction unit 1706 generates a feedback signal of an error countas information for the decision of a next initial position. The controlcircuit 1703 generates control signals for the polarization transformer1701 and the adaptive optics 1702 using the feedback signals from thepolarimeter 1704 and the forward error correction unit 1706.

As described in detail above, according to the present invention, apolarization control that is tolerant to changing device characteristicsof a PMDC with environmental changes and time is provided. Therefore, itis possible to adjust the PMDC to its optimum state even in the casewhere the device characteristics change.

1. A polarization mode dispersion compensator comprising: a polarizationtransformer to transform polarization of an input optical signal; acompensating optical unit to compensate for a polarization modedispersion of the input optical signal and output an output opticalsignal; a polarimeter to measure a state of polarization and a degree ofpolarization of the output optical signal and generate a feedback signalindicating the measured state of polarization and degree ofpolarization; and a control circuit to generate, based on the feedbacksignal, control signals for adjusting the polarization transformer insuch a way that a plurality of target states of polarization in whichthe degree of polarization is measured are realized in output opticalsignals in following operations.
 2. The polarization mode dispersioncompensator according to claim 1, wherein the polarization transformeris realized by multiple three-electrode structures on a LiNbO₃substrate, whereby control voltages are applied such that a deviceoperation of the polarization transformer corresponds to endlessrotatable waveplates.
 3. The polarization mode dispersion compensatoraccording to claim 1, wherein the compensating optical unit is realizedin such a way that an amount of differential group delay is introducedby one of a polarization maintaining fiber and a birefringent crystal.4. The polarization mode dispersion compensator according to claim 1,wherein the compensating optical unit comprises a plurality of sectionsof differential group delay introducing elements separated by at leastone individually controllable variable retarder with an eigenaxisoriented at an angle of 45 degree with respect to an eigenaxis of eachof two adjacent differential group delay introducing elements.
 5. Thepolarization mode dispersion compensator according to claim 1, whereinthe control circuit generates the control signals for adjusting thepolarization transformer in such a way that an optimum state is foundfrom among the target states of polarization by searching for a statewith the maximum degree of polarization in a circumference of an actualstate in a polarization space.
 6. The polarization mode dispersioncompensator according to claim 5, wherein the control circuit recordsthe measured state of polarization and degree of polarization, andcalculates from polarization changes control signals for adjusting thepolarization transformer in such a way that the target states ofpolarization are equally separated from each other and equally distantfrom the actual state in the polarization space.
 7. The polarizationmode dispersion compensator according to claim 6, wherein the targetstates of polarization are preset and located on a circle around theactual state at a predefined distance in the polarization space.
 8. Thepolarization mode dispersion compensator according to claim 5, whereinthe control circuit records the measured state of polarization anddegree of polarization, calculates from polarization changes controlsignals for adjusting the polarization transformer in such a way thatthe target states of polarization are unequally separated from eachother and unequally distant from the actual state in the polarizationspace, and weights measured degrees of polarization in the target statesof polarization by using a distance between each target state ofpolarization and the actual state in the polarization space.
 9. Thepolarization mode dispersion compensator according to claim 1, whereinthe control circuit recognizes changing device characteristics of thepolarization transformer in a case where a part of the target states ofpolarization are not realized, and takes countermeasures such that thepolarization transformer operates like endless rotatable waveplates byrecalculating a voltage which describes the device characteristics ofthe polarization transformer and generating a control signal forapplying the calculated voltage to the polarization transformer.
 10. Apolarization mode dispersion compensator comprising: a polarizationtransformer to transform polarization of an input optical signal; acompensating optical unit to compensate for a polarization modedispersion of the input optical signal and output an output opticalsignal; a distortion analyzer to measure a state of polarization and adistortion of the output optical signal and generate a feedback signalindicating the measured state of polarization and distortion; and acontrol circuit to generate, based on the feedback signal, controlsignals for adjusting the polarization transformer in such a way that aplurality of target states of polarization in which the distortion ismeasured are realized in output optical signals in following operations.11. A method of polarization mode dispersion compensation, comprising:transforming polarization of an input optical signal through apolarization transformer; compensating for a polarization modedispersion of the input optical signal through a compensating opticalunit to generate an output optical signal; measuring a state ofpolarization and a distortion of the output optical signal to generate afeedback signal indicating the measured state of polarization anddistortion; and adjusting the polarization transformer according to thefeedback signal in such a way that a plurality of target states ofpolarization in which the distortion is measured are realized in outputoptical signals in following operations.